{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "tags": [
     "remove-cell"
    ]
   },
   "outputs": [],
   "source": [
    "import sys\n",
    "import os\n",
    "if not any(path.endswith('textbook') for path in sys.path):\n",
    "    sys.path.append(os.path.abspath('../../..'))\n",
    "from textbook_utils import *          "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "tags": [
     "remove-cell"
    ]
   },
   "outputs": [],
   "source": [
    "from sklearn.linear_model import LinearRegression\n",
    "from sklearn.metrics import mean_squared_error, r2_score\n",
    "from sklearn.model_selection import train_test_split, cross_val_score\n",
    "from sklearn import model_selection"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Regularization\n",
    "\n",
    "\n",
    "We just saw how cross-validation can help find a dimension for a fitted model that balances under- and overfitting. Rather than selecting the dimension of the model, we can build a model with all of the features, but restrict the size of the coefficients. We keep from overfitting by adding to the MSE a penalty term on the size of the coefficients. The penalty, called a *regularization term*, is $ \\lambda \\sum_{j = 1}^{p} \\theta_j^2 $. We fit the model by minimizing the combination of mean squared error plus this penalty:\n",
    "\n",
    "$$\n",
    "\\frac{1}{n} \\sum_{i=1}^{n}(y_i - \\mathbf{x}_i \\boldsymbol{\\theta})^2  ~+~ \\lambda \\sum_{j = 1}^{p} \\theta_j^2\n",
    "$$\n",
    "\n",
    "When the *regularization parameter*, $\\lambda$, is large, it penalizes large coefficients.\n",
    "(We typically choose it by cross-validation.) \n",
    "\n",
    "Penalizing the square of the coefficients is called $ L_2 $ regularization, or *ridge regression*. Another popular regularization penalizes the absolute size of the coefficients: \n",
    "\n",
    "$$\n",
    "\\begin{aligned}\n",
    "\\frac{1}{n} \\sum_{i=1}^{n}(y_i - \\mathbf{x}_i \\boldsymbol{\\theta})^2  ~+~ \\lambda \\sum_{j = 1}^{p} |\\theta_j|\n",
    "\\end{aligned}\n",
    "$$\n",
    "\n",
    "This  $ L_1 $ regularized linear model is also called *lasso regression* (lasso stands for Least Absolute Shrinkage and Selection Operator).\n",
    "\n",
    "To get an idea about how regularization works, let's think about the extreme cases: when $ \\lambda $ is really large and when it's close to 0 ($ \\lambda $ is never negative). With a big regularization parameter, the coefficients are heavily penalized, so they shrink. On the other hand, when $ \\lambda $ is tiny, the coefficients aren't restricted. In fact, when $ \\lambda $ is 0, we're back in the world of ordinary least squares. A couple of issues crop up when we think about controlling the size of the coefficients through regularization: \n",
    " \n",
    "+ We do not want to regularize the intercept term. This way, a large penalty fits a constant model.\n",
    "+ When features have very different scales, the penalty can impact them differently, with large-valued features being penalized more than others. To avoid this, we standardize all of the features to have mean 0 and variance 1 before fitting the model.\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's look at an example with 35 features."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Example: A Market Analysis\n",
    "\n",
    "A [market research project](https://doi.org/10.1080/02664763.2014.994480) for a pharmaceutical company wants to model consumer interest in purchasing a cold sore health-care product. They gather data from 1,023 consumers. Each consumer is asked to rate on a 10-point scale 35 factors according to whether the factor matters to them when considering purchasing a cold sore treatment. They also rate their interest in purchasing the product.[^Lipovetsky] \n",
    "\n",
    "[^Lipovetsky]: Stan Lipovetsky and W. Michael Conklin (2015) Predictor relative importance\n",
    "and matching regression parameters. _Journal of Applied Statistics_, 42:5, 1017-1031."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We begin by reading in the data:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "ma_df = pd.read_csv('data/market-analysis.csv')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "{numref}`Table %s <market-codebook>` lists the 35 factors and provides their correlation to the outcome, their interest in purchasing the product. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    ":::{table} Codebook\n",
    ":name: market-codebook\n",
    "\n",
    "\n",
    "|  | Corr | Description |  | Corr | Description |\n",
    "| --- | --- | --------- | --- | --- | --------- |\n",
    "| x1  | 0.70 | provides soothing relief | x19 | 0.54 | has a non-messy application |\n",
    "| x2  | 0.58 | moisturizes cold sore blister | x20 | 0.70 | good for any stage of a cold |\n",
    "| x3  | 0.69 | provides long-lasting relief | x21 | 0.49 | easy to apply/take |\n",
    "| x4  | 0.70 | provides fast-acting relief | x22 | 0.52 | package keeps from contamination |\n",
    "| x5 | 0.72 | shortens duration of a cold | x23 | 0.57 | easy to dispense a right amount |\n",
    "| x6  | 0.68 | stops the virus from spreading | x24 | 0.63 | worth the price it costs |\n",
    "| x7 | 0.67| dries up cold sore | x25 | 0.57 | recommended most by pharamacists |\n",
    "| x8 | 0.72 | heals fast | x26 | 0.54 | recommended by doctors |\n",
    "| x9 | 0.72 | penetrates deep | x27 | 0.54 | FDA approved |\n",
    "| x10 | 0.65 | relieves pain | x28 | 0.64 | a brand I trust |\n",
    "| x11 |0.61 | prevents cold | x29 | 0.60 | clinically proven |\n",
    "| x12 | 0.73 | prevents from getting worse | x30 | 0.68 | a brand I would recommend |\n",
    "| x13 | 0.57 | medicated | x31 | 0.74 | an effective treatment |\n",
    "| x14 | 0.61 | prescription strength | x32  |0.37 | portable |\n",
    "| x15 | 0.63 | repairs damaged skin | x33 | 0.37 | discreet packaging |\n",
    "| x16 | 0.67 | blocks virus from spreading | x34 | 0.55 | helps conceal cold sores |\n",
    "| x17 | 0.42 | contains SPF | x35 | 0.63 | absorbs quickly |\n",
    "| x18 | 0.57 | non-irritating | | | |\n",
    "\n",
    ":::"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Based on their labels alone, some of these 35 features appear to measure similar aspects of desirability. We can compute the correlations between the explanatory variables to confirm this: "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 213,
   "metadata": {
    "tags": [
     "remove-input"
    ]
   },
   "outputs": [
    {
     "data": {
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       "      <td>0.81</td>\n",
       "      <td>0.75</td>\n",
       "      <td>0.73</td>\n",
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       "      <td>0.57</td>\n",
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       "      <td>0.65</td>\n",
       "      <td>0.63</td>\n",
       "      <td>0.63</td>\n",
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       "      <th>x33</th>\n",
       "      <td>0.37</td>\n",
       "      <td>0.33</td>\n",
       "      <td>0.36</td>\n",
       "      <td>0.34</td>\n",
       "      <td>0.32</td>\n",
       "      <td>0.32</td>\n",
       "      <td>0.37</td>\n",
       "      <td>...</td>\n",
       "      <td>0.39</td>\n",
       "      <td>0.41</td>\n",
       "      <td>0.35</td>\n",
       "      <td>0.34</td>\n",
       "      <td>1.00</td>\n",
       "      <td>0.35</td>\n",
       "      <td>0.36</td>\n",
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       "    <tr>\n",
       "      <th>x34</th>\n",
       "      <td>0.55</td>\n",
       "      <td>0.57</td>\n",
       "      <td>0.55</td>\n",
       "      <td>0.67</td>\n",
       "      <td>0.60</td>\n",
       "      <td>0.59</td>\n",
       "      <td>0.64</td>\n",
       "      <td>...</td>\n",
       "      <td>0.58</td>\n",
       "      <td>0.48</td>\n",
       "      <td>0.58</td>\n",
       "      <td>0.16</td>\n",
       "      <td>0.35</td>\n",
       "      <td>1.00</td>\n",
       "      <td>0.54</td>\n",
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       "      <th>x35</th>\n",
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       "      <td>0.71</td>\n",
       "      <td>0.63</td>\n",
       "      <td>0.70</td>\n",
       "      <td>0.72</td>\n",
       "      <td>0.69</td>\n",
       "      <td>0.68</td>\n",
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       "      <td>0.36</td>\n",
       "      <td>0.54</td>\n",
       "      <td>1.00</td>\n",
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       "        y    x1    x2    x3    x4    x5    x6  ...   x29   x30   x31   x32  \\\n",
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       "x2   0.58  0.69  1.00  0.63  0.65  0.63  0.63  ...  0.60  0.62  0.66  0.43   \n",
       "..    ...   ...   ...   ...   ...   ...   ...  ...   ...   ...   ...   ...   \n",
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       "x34  0.55  0.57  0.55  0.67  0.60  0.59  0.64  ...  0.58  0.48  0.58  0.16   \n",
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       "      x33   x34   x35  \n",
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       "x2   0.36  0.55  0.63  \n",
       "..    ...   ...   ...  \n",
       "x33  1.00  0.35  0.36  \n",
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       "\n",
       "[36 rows x 36 columns]"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "display_df(ma_df.corr(), cols=14)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We see, for example, that the last feature, \"absorbs quickly,\" is highly correlated with the first three: \"provides soothing relief,\" \"moisturizes,\" and \"provides long-lasting relief.\"   "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Before we start to fit regularized models, we set up the design matrix and outcome vector and split the data into train and test sets. We place 200 observations in the test set:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "y = ma_df[\"y\"]\n",
    "X = ma_df.drop(columns=[\"y\"])\n",
    "\n",
    "X_train, X_test, y_train, y_test = train_test_split(\n",
    "    X, y, test_size=200, random_state=42\n",
    ")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "As mentioned earlier, we need to standardize the features. We standardize the train set, and then, when we go to evaluate the model, we use the train set standardization on the test set. The `StandardScaler` method helps us with this process:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "from sklearn.preprocessing import StandardScaler\n",
    "\n",
    "scalerX = StandardScaler().fit(X_train) \n",
    "X_train_scaled = scalerX.transform(X_train)\n",
    "X_test_scaled = scalerX.transform(X_test)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We confirm that the means of the 35 features in the train set are all 0 and the SDs are all&nbsp;1: "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 220,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "True"
      ]
     },
     "execution_count": 220,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.allclose(X_train_scaled.mean(axis=0), 0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 222,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "True"
      ]
     },
     "execution_count": 222,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.allclose(X_train_scaled.std(axis=0), 1)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "It's important to note that this is not the case for the test set, because we\n",
    "use the averages and SDs from the train set to standardize the test set features:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 224,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([-0.17, -0.12, -0.15, ..., -0.12, -0.1 , -0.24])"
      ]
     },
     "execution_count": 224,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "X_test_scaled.mean(axis=0)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "To perform a lasso regression, we use the `Lasso` method in `scikit-learn`.  Let's see how the coefficients for the 35 features in the data frame change with $\\lambda$. We set up a range of values for the regularization parameter and fit the lasso for each (this parameter is referred to as `alpha` in `Lasso`): "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "from sklearn.linear_model import Lasso\n",
    "\n",
    "coefs = []\n",
    "mses = []\n",
    "alphas = np.arange(0.01, 2, 0.01)\n",
    "\n",
    "for a in alphas:\n",
    "    model = Lasso(alpha=a)\n",
    "    model.fit(X_train_scaled, y_train)\n",
    "    coefs.append(model.coef_)\n",
    "    mses.append(mean_squared_error(y_test, model.predict(X_test_scaled)))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "For each feature, we can overlay a line plot of the coefficient against $ \\lambda $: "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "tags": [
     "remove-input"
    ]
   },
   "outputs": [
    {
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           "gridcolor": "rgb(232,232,232)",
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           "title": {
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        "xaxis": {
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         "autorange": true,
         "domain": [
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         "range": [
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         "title": {
          "text": "Lambda"
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         "type": "log"
        },
        "yaxis": {
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         "autorange": true,
         "domain": [
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         "range": [
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         "title": {
          "text": "Coefficient"
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         "type": "linear"
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   "source": [
    "col_names = [\"x\" + str(v) for v in np.arange(1, 36, 1)]\n",
    "\n",
    "coefs_df = pd.DataFrame(coefs, columns=col_names)\n",
    "\n",
    "coefs_df[\"lambda\"] = alphas\n",
    "coefs_long = pd.melt(coefs_df, id_vars=[\"lambda\"], value_vars=col_names)\n",
    "\n",
    "fig = px.line(coefs_long, x=\"lambda\", y=\"value\", color=\"variable\", log_x=True)\n",
    "fig.update_layout(\n",
    "    showlegend=False, width=550, height=250, yaxis_title=\"Coefficient\",\n",
    "    xaxis_title=\"Lambda\"\n",
    ")"
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   "source": [
    "As $ \\lambda $ increases, the model fitting is penalized more heavily and many coefficients shrink to 0. The lefthand side of the plot shows greater model complexity and corresponds to small $ \\lambda $. Notice that for $ \\lambda = 0.5 $, nearly all of the coefficients are 0. The exceptions are, from largest to smallest: `x12`, `x30`, `x31`, `x5`, `x7`,  `x1`, `x9`,  `x28`, `x20`. \n",
    "\n",
    "We can also plot the MSE as a function of $ \\lambda $ to see how it changes with the increase in the penalty:"
   ]
  },
  {
   "cell_type": "code",
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   ],
   "source": [
    "px.line(x=alphas, y=mses,\n",
    "        labels={\"x\": \"Lambda\", \"y\": \"MSE\"},\n",
    "        width=350, height=250)"
   ]
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   "cell_type": "markdown",
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   "source": [
    "When $ \\lambda $ reaches about 1.25, the penalty is so large that the lasso regression is simply fitting a constant model to the data, and the MSE doesn't change. We are again faced with a model selection question, but this time it's in the form of deciding on $ \\lambda $. We can use cross-validation to help us. \n",
    "\n",
    "We use the `LassoCV` method to perform 5-fold cross-validation to choose $\\lambda$:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [],
   "source": [
    "from sklearn.linear_model import LassoCV\n",
    "\n",
    "lasso_cv_model = LassoCV(\n",
    "    alphas=np.arange(0.01, 1, 0.01), cv=5, max_iter=100000\n",
    ")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Notice that we have specified a maximum number of iterations because the minimization uses numerical optimization (see {numref}`Chapter %s <ch:gd>`) to solve for the coefficients, and we have placed a cap on the number of iterations to run to reach the specified tolerance for the optimal parameter. We're ready to fit the model on the train set:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [],
   "source": [
    "lasso_best = lasso_cv_model.fit(X_train_scaled, y_train)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Cross-validation has chosen the following regularization parameter:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 240,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.04"
      ]
     },
     "execution_count": 240,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "lasso_best.alpha_"
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  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Next, let's compute the MSE for predictions in the test set using this cross-validated model: "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1.0957444655340487"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "y_test_pred = lasso_best.predict(X_test_scaled)\n",
    "mean_squared_error(y_test, y_test_pred)"
   ]
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  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's find how many coefficients are not 0:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 243,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "16"
      ]
     },
     "execution_count": 243,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sum(np.abs(lasso_best.coef_) > 0)"
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   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We next demonstrate how the ridge regression coefficients change with the penalty. Ridge regression uses an $ L_2 $ penalty, but otherwise the implementation is similar to lasso regression. As before, we try a range of $ \\lambda $ values and then plot the coefficients to see how they change: "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [],
   "source": [
    "from sklearn.linear_model import Ridge\n",
    "\n",
    "coefsR = []\n",
    "alphasR = np.arange(1, 1001, 25)\n",
    "\n",
    "for a in alphasR:\n",
    "    ridge = Ridge(alpha=a)\n",
    "    ridge.fit(X_train_scaled, y_train)\n",
    "    coefsR.append(ridge.coef_)"
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   "execution_count": 13,
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            "showgrid": false,
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          },
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            "linecolor": "rgb(36,36,36)",
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          "title": {
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           "xanchor": "center"
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          "xaxis": {
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           "gridcolor": "rgb(232,232,232)",
           "linecolor": "rgb(36,36,36)",
           "showgrid": true,
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           "ticks": "outside",
           "title": {
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           },
           "zeroline": false,
           "zerolinecolor": "rgb(36,36,36)"
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           "gridcolor": "rgb(232,232,232)",
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        "width": 550,
        "xaxis": {
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         "autorange": true,
         "domain": [
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         ],
         "range": [
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         "title": {
          "text": "Lambda"
         },
         "type": "log"
        },
        "yaxis": {
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         "autorange": true,
         "domain": [
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         "range": [
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         "title": {
          "text": "Coefficient"
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         "type": "linear"
        }
       }
      },
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    "coefsR = np.squeeze(coefsR)\n",
    "\n",
    "col_names = [\"x\" + str(v) for v in np.arange(1, 36, 1)]\n",
    "\n",
    "coefsR_df = pd.DataFrame(coefsR, columns=col_names)\n",
    "coefsR_df[\"lambda\"] = alphasR\n",
    "\n",
    "coefsR_long = pd.melt(coefsR_df, id_vars=[\"lambda\"], value_vars=col_names)\n",
    "\n",
    "fig = px.line(coefsR_long, x=\"lambda\", y=\"value\", color=\"variable\", log_x=True)\n",
    "fig.update_layout(\n",
    "    showlegend=False, width=550, height=250, \n",
    "    yaxis_title=\"Coefficient\", xaxis_title=\"Lambda\"\n",
    ")\n",
    "fig.show()"
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    "This plot shows a very different shape compared to the lasso coefficient plot. The coefficients do not disappear entirely. The plots do have an important similarity in that as the penalty increases, the coefficients shrink.  In a way, with ridge regression, we are using all of the variables a little bit. For large $ \\lambda $, many coefficients, while not 0, are quite small. For example, we can count the number of coefficients larger than 0.05 for $ \\lambda = 600 $:"
   ]
  },
  {
   "cell_type": "code",
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    {
     "data": {
      "text/plain": [
       "13"
      ]
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     "execution_count": 246,
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   "source": [
    "sum(abs(coefsR[24, :]) > 0.05)"
   ]
  },
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   "metadata": {
    "tags": []
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   "source": [
    "Similar to lasso, many of the features have tiny coefficients."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Again, to select the best $ \\lambda $ we can turn to cross-validation and use `RidgeCV`. We omit the details here because the approach is the same as `LassoCV`."
   ]
  },
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   "cell_type": "markdown",
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    "Using $ L_1 $ or $ L_2 $ regularization allows us to avoid model overfitting by penalizing large coefficients.  $ L_1 $ regularization has the advantage of zeroing out coefficients; it performs *feature selection* by discarding the features with a coefficient of 0. This is particularly useful when working with high-dimensional data with many features. A model that only uses a few features to make a prediction runs much faster than a model that requires many calculations. Since unneeded features tend to increase model variance without decreasing bias, we can sometimes increase the accuracy of other models by using lasso regression to select a subset of features to use."
   ]
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    ":::{note}\n",
    "\n",
    "Sometimes we prefer one type of regularization over the other because it maps more closely to the domain we are working with. For example, if we know that the phenomenon we are trying to model results from many small factors, we might prefer ridge regression because it won't discard these factors. On the other hand, some outcomes result from a few highly influential features. We prefer lasso regression in these situations because it discards unneeded features. Both $L_2$ and $L_1$ serve as useful throttles to navigate between under- and overfitting.\n",
    "\n",
    ":::"
   ]
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   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Regularization, train-test split, and cross-validation all have the goal of reducing over-fitting. The problem with over-fitting comes from using data to both fit a model and estimate the model's error in predicting new observations. In the next section, we provide further intuition for this idea."
   ]
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